Outside of a rare mutation, the most menacing influenza, the one that fits in this class, is H5N1, which for unknown reasons has not yet become easily H2H transmissible. Very atypically, since it was discovered it has maintained a 60% mortality rate. It is the nuclear weapon of epidemics.
The only epidemic that has come close to that in any mammal was the myxomatosis plague in Australian rabbits in the 1950s.
H5N1 only had about 500 human victims, iirc. There were a couple of H2H cases, but the nature of the virus is such that it prefers deep lung temperatures over cooler upper respiratory ones and thus is harder to transmit through the usual sneezing and coughing, etc.